The quantitative human health risk assessment (AqR) due a contaminated site has became an important tool at Environmental Managenment and at the identification of environmental harm, at Brazil and other countries. The AqR procedures consists in logical sequence of actions concerned about legal aspects, toxicological matter and transport phenomena. In spite of the absence of a single law that could regulate specifically the AqR, the Environmental Law, as a whole, allows that AqR methodologies to be fully applied at governamental and judicial levels. The AqR procedures are base on pharmaco-kinetics models that quantitatively relates the exposure to the chemicals to human harm potency. The Environmental Geotechnics studies the fate and transport of contaminants at soil and groundwater. AqR is complex and full of uncertainties and variabilities subject. It have been proposed the application of the first order second moment method (FOSM) to quantify the uncertainties related to the estimation of the transport parameters to be used in the analytical transport model of solute in porous media (Domenico). It have been developed a specific software that meets this objective (SeRis). This software proved to be computationally efficient. The case study example indicated the relative importance of the considered parameters and presented a reasonable total system variance.